Question

Gender and Divorce. According to America's Families and Living Arrangements, published by the U.S. Census Bureau, 51.5% of U.S. adults are female, 10.4% of U.S. adults are divorced, and 6.0% of U.S. adults are divorced females. For a U.S. adult selected at random, let F = event the person is female, and D = event the person is divorced. a. Obtain P(F), P(D), and P(F & D). b. Determine P(F or D), and interpret your answer in terms of percentages. c. Find the probability that a randomly selected adult is male. d. Find the probability that a randomly selected adult is male or divorced, P(M or D) 2. Suppose that A and B are events such that P(A) = 1/4, P(B) = 1/3, and P(A or B) = 1/2. a.Are events A and B mutually exclusive? Explain your answer. b.Find P(A & B). c. Find P(A or B)

Answer 1

(1) Percentage of adults that are females = 51.5%

Percentage of adults that are males = 100 - 51.5 = 48.5%

Percentage of adults that are divorced = 10.4%

Percentage of divorced females = 6.0%

Percentage of divorced males = 10.4 - 6 = 4.4%

F = event that the person is female = 51.5%

D = event that the person is divorced = 10.4%

(a) P(F) = 51.5%

P(D) = 10.4%

P(F and D) = 6.0%

(b) P(F or D) = P(F) +P(D) - P(F and D)

= 51.5 + 10.4 - 6.0

= 55.9%

(c) Probability that randomly selected adult is male = 48.5%

(d) P (M or D) = P(M) + P(D) - P(M and D)

= 48.5 + 10.4 - 4.4

= 54.5%

(2) P(A) = 1/4

P(B) = 1/3

P(A or B) = 1/2

(a) If the events are mutually exclusive events, they should follow the following rule:-

P(A or B) = P(A) + P(B)

1/2 ≠ 1/4 + 1/3

So, they are not mutually exclusive events

(b) P(A and B) = P(A) + P(B) - P(A or B)

= 1/4 + 1/3 - 1/2

= 0.08 or 2/25

(c) P (A or B) = 1/2